In the first cast study, we determine the maximum threshold velocity of the top plate \(U\)  in a lid-driven cavity flow at various relaxation times \(\tau \)  for RNR-LBM and RC-LBM using the rectangular lattice with grid aspect ratios of \(a= 1.0, 0.5\) , and \(0.3\) . These aspect ratios correspond to choosing fixed
coarse grid resolutions of \(21\times 21\) , \(21\times 41\)  and \(21\times 61\) , respectively. Following a strategy similar to Refs. [1]}, [2]}, we evaluate the maximum lid velocity which maintains stable simulations for 100,000 time steps for the rectangular LB formulations. Figure REF  shows the stability regime results for RNR-LBM and RC-LBM for different choices of \(a\) . It can be seen that, in general, as the grid aspect ratio decreases, characterized by greater geometric anisotropy of the lattice, the numerically stable regime becomes narrower. However, in all cases, the RC-LBM based on central moments is found to be significantly more stable compared to the RNR-LBM based on raw moments, with the former generally taking a relatively small additional computational overhead of about \(25\%\)  when compared to the former.
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